all tags for a category in a linked list

<?php
    query_posts('category_name=work');
    if (have_posts()) : while (have_posts()) : the_post();
        $posttags = get_the_tags();
        if ($posttags) {
            foreach($posttags as $tag) {
                $all_tags_arr[] = $tag->term_id; //USING JUST $tag MAKING $all_tags_arr A MULTI-DIMENSIONAL ARRAY, WHICH DOES WORK WITH array_unique
            }
        }
    endwhile; endif; wp_reset_query();

    $tags_arr = array_unique($all_tags_arr); //REMOVES DUPLICATES
    //echo '<pre>'.print_r($tags_arr, true).'</pre>'; //OUTPUT FINAL TAGS FROM CATEGORY

echo '<ul>';
foreach ($tags_arr as $tag) {
echo '<li><a href="' . get_tag_link($tag) . '">' . get_tag($tag)->name . '</a></li>';
}
echo '</ul>';

?>